Can we measure structures to a precision better than the Planck length?

Hossenfelder, Sabine

doi:10.1088/0264-9381/29/11/115011

Cited by 54 publications

(37 citation statements)

References 24 publications

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“…in view of the fact that our background is now by assumption minkowskian. Note that in order to ensure that in the spherical case (∆x 1 = ∆x 2 = ∆x 3 = 2∆R with obvious notation) we have A = 4π∆R 2 , we need to take β 2 = 3/(π) [15]. We estimate the energy of the collapsing field configuration making use of Heisenberg's uncertainty relations…”

Section: For Asymptotically Flat Data Horizons Form If and Only Ifmentioning

confidence: 99%

“…where of course ∆ ω A is just a shorthand as in (8). It is obtained by making use of inequality (15) to eliminate the dependence on the three-volume ∆ ω V in (24) and substituting √ ∆A ≤ ∆η i in (25). For the sake of definiteness, we collect below some desirable properties of a "concrete quantum model".…”

Section: Models Of Quantum Expanding Spacetimesmentioning

confidence: 99%

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Building non-commutative spacetimes at the Planck length for Friedmann flat cosmologies

Tomassini

Viaggiu²

2014

Class. Quantum Grav.

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We propose physically motivated spacetime uncertainty relations (STUR) for flat Friedmann-Lemaître cosmologies. We show that the physical features of these STUR crucially depend on whether a particle horizon is present or not. In particular, when this is the case we deduce the existence of a maximal value for the Hubble rate (or equivalently for the matter density), thus providing an indication that quantum effects may rule out a pointlike big bang singularity. Finally, we costruct a concrete realisation of the corresponding quantum Friedmann spacetime in terms of operators on a Hilbert space.

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Section: For Asymptotically Flat Data Horizons Form If and Only Ifmentioning

confidence: 99%

Section: Models Of Quantum Expanding Spacetimesmentioning

confidence: 99%

Building non-commutative spacetimes at the Planck length for Friedmann flat cosmologies

Tomassini

Viaggiu²

2014

Class. Quantum Grav.

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“…In the HUP framework, the restriction upon the position measurement precision does not exist. On the contrary, in the GUP framework that can be regarded as a phenomenological description of quantum gravity effects, a minimal position measurement precision is predicted with the order of the Planck length ℓ Pl = G /c 3 ∼ 10 −33 cm below which the spacetime cannot be probed effectively [10,11,12,13]. In other words, a finite resolution appears in the spacetime.…”

Section: Introductionmentioning

confidence: 98%

Maximally Localized States and Quantum Corrections of Black Hole Thermodynamics in the Framework of a New Generalized Uncertainty Principle

Miao

Zhao

Zhang

2015

Advances in High Energy Physics

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As a generalized uncertainty principle (GUP) leads to the effects of the minimal length of the order of the Planck scale and UV/IR mixing, some significant physical concepts and quantities are modified or corrected correspondingly. On the one hand, we derive the maximally localized states -the physical states displaying the minimal length uncertainty associated with a new GUP proposed in our previous work. On the other hand, in the framework of this new GUP we calculate quantum corrections to the thermodynamic quantities of the Schwardzschild black hole, such as the Hawking temperature, the entropy, and the heat capacity, and give a remnant mass of the black hole at the end of the evaporation process. Moreover, we compare our results with that obtained in the frameworks of several other GUPs. In particular, we observe a significant difference between the situations with and without the consideration of the UV/IR mixing effect in the quantum corrections to the evaporation rate and the decay time. That is, the decay time can greatly be prolonged in the former case, which implies that the quantum correction from the UV/IR mixing effect may give rise to a radical rather than a tiny influence to the Hawking radiation.

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“…Some physicists would claim they are just mathematical artifacts with no implications for physics whatsoever, while others think there could be a unit smaller than the Planck length (Agarwal & Pathak, 2004;Ghosh, Roy, Genes, & Vitali, 2009;Zurek, 2001), and still others maintain that there should be no minimum length at all -that zero is the minimum. Nevertheless, the majority of physicists seem to agree that there is a minimum length and that it likely is the Planck length (see Adler, 2010;Ali, Khalil, & Vagenas, 2015;Garay, 1995;Hossenfelder, 2012;Padmanabhan, 1985). Later in this paper, we will point out recent progress in physics strongly indicating that the Planck length is indeed truly essential, and something that we can observe without relying on the Planck length formula.…”

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confidence: 80%

Does Special Relativity Lead to a Trans-Planckian Crisis?

Haug¹

2019

APR

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In gravity theory, there is a well-known trans-Planckian problem, which is that general relativity theory leads to a shorter than Planck length and shorter than Planck time in relation to so-called black holes. However, there has been little focus on the fact that special relativity also leads to a trans-Planckian problem, something we will demonstrate here. According to special relativity, an object with mass must move slower than light, but special relativity has no limits on how close to the speed of light something with mass can move. This leads to a scenario where objects can undergo so much length contraction that they will become shorter than the Planck length as measured from another frame, and we can also have shorter time intervals than the Planck time.The trans-Planckian problem is easily solved by a small modification that assumes Haug's maximum velocity for matter is the ultimate speed limit for something with mass. This speed limit depends on the Planck length, which can be measured without any knowledge of Newton's gravitational constant or the Planck constant.

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Can we measure structures to a precision better than the Planck length?

Cited by 54 publications

References 24 publications

Building non-commutative spacetimes at the Planck length for Friedmann flat cosmologies

Building non-commutative spacetimes at the Planck length for Friedmann flat cosmologies

Maximally Localized States and Quantum Corrections of Black Hole Thermodynamics in the Framework of a New Generalized Uncertainty Principle

Does Special Relativity Lead to a Trans-Planckian Crisis?

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